Search

To avoid numerical inaccuracy of the transient solution by the time-domain solvers or frequency-domain solvers, a simultaneous extrapolation approach reconstructing of the wide-band frequency spectrum using low-frequency and early-time data by the local linear basis functions is presented. The basic idea is transforming the transient integral equations into the analytical-form matrix equation, which can be solved using basis functions with a local support. By means of the early-time and low-frequency data, the matrix equation is solved by the method of singular value decomposition to obtain the wide-band spectrum. The proposed approach is validated by several numerical examples and applied in calculating the transient horizontal electric field of a lightning channel. The major advantage of the presented approach is an efficient and stable algorithm that can be generalized to apply to other transient scenarios when frequency- and time-domain-based transient analysis are involved.

Using the multiple-model~(MM) probability hypothesis density~(PHD) filter, millimeter wave~(mmWave) radio simultaneous localization and mapping~(SLAM) in vehicular scenarios is susceptible to movements of objects, in particular vehicles driving in parallel with the ego vehicle. We propose and evaluate two countermeasures to track vehicle scatterers~(VSs) in mmWave radio MM-PHD-SLAM. First, locally at each vehicle, we generate and treat the VS map PHD in the context of Bayesian recursion, and modify vehicle state correction with the VS map PHD. Second, in the global map fusion process at the base station, we average the VS map PHD and upload it with self-vehicle posterior density, compute fusion weights, and prune the target with low Gaussian weight in the context of arithmetic average-based map fusion. From simulation results, the proposed cooperative mmWave radio MM-PHD-SLAM filter is shown to outperform the previous filter in VS scenarios.

Building HVdc and HVac transmission lines in the same corridor or even on the same tower is an attractive way to extend electricity transport capacity where getting the new right of way is difficult. The resulting hybrid lines produce a new corona performance, such as ground-level hybrid electric field and ion current density, which are quite different from those of pure ac or dc lines. In this paper, inherent space-time pattern and characteristics of the information propagation in Lagrangian description are presented for the ion transport problem, that is, the ion density at a certain point has a direct relationship with its drift time. Based on this, the theoretical explanation is provided for the decoupling algorithm, by which the ground-level dc component can be solved with the ac conductors assumed to be at zero potential and vice versa. The simulation results show that the sinusoidal ac field has negligible influence on the dc ion drift time from conductor surface to ground, whereas stationary electric field generated by the grounded ac lines has a dominant effect. Therefore, ac energization has a rather low impact on ground-level quantities and the simplification of grounded ac conductors is quite reasonable.

The ion-flow environment is an important corona design factor of HVDC transmission lines. The space charges generated by corona form a typical convection-dominated ion-flow field. For this special transport phenomenon, however, standard Galerkin FEM always presents serious deficiencies. In this study, a new approach is used to solve ion-flow field based on Petrov–Galerkin method derived from the theory of fluid computation. A high-order stabilisation technique is used to overcome the non-physical oscillations in the presence of highly convective effects. This algorithm is equivalent to the proper modification of weight function according to the direction and magnitude of local drift velocity. It reflects the characteristic of information propagation in flow problem. The establishment procedure of weak form and matrix gives a further explanation on the deficiency of Galerkin method. Moreover, to guarantee convergence of the iteration for this fully-coupled non-linear problem, a relaxation method is introduced in the iterative loop. Calculations with the Petrov–Galerkin least square method are in good agreement with analytical solution and experiment values of ground-level values and corona losses. Results show that the proposed stabilisation technique is able to preclude the numerical spurious oscillation and has a higher-order accuracy than the fully-upwind treatment.

The evaluation of the ground admittance of an underground insulated conductor with a homogeneous nonmagnetic earth is of great significance when the electromagnetic compatibility is concerned. To evaluate the ground admittance efficiently, researchers proposed that the ground impedance of the conductor should be evaluated first and the ground admittance is related to the ground impedance through the wave number in the soil. There are several approximated analytical expressions for the evaluation of the ground impedance with a homogeneous earth and this fact makes the ground admittance easy to obtain. The characteristic of the approximated ground admittance evaluation approach is examined in this paper. Numerical examples illustrate that at frequencies with which the burial depth is much larger than the skin depth in the soil, the ground admittance and the ground impedance of the buried cable are well-related through the wave number in the soil. However, at other frequencies, the approximated approach fails to evaluate the ground admittance accurately. This paper also reveals that the discrepancy of the ground admittance will lead to a noticeable difference in the lightning induced voltage on buried cables.

The electric field and ion flow are significantly influenced by the transverse wind around the high-voltage direct current (HVDC) transmission lines. In this study, a new method using local characteristics is proposed to analyse the effect of wind. The present method, called method of local characteristic, updates the ion density based on the local characteristic curve in each second-order finite element method (FEM) element without Deutsch assumption. The defining equation of the characteristics is able to take into account the directional character of the information propagation in convective transport and has a better performance to satisfy the conservation law. The present approach is stable and efficient even in the presence of high-speed transverse wind. Calculations show good agreement with the measurement values of the reduced-scale unipolar model and the full-scale bipolar test line. Finally, the influence of wind on the electric field and ion current is discussed.

The evaluation of the earth return mutual impedance of arbitrary conductor arrangements with a horizontally multilayered nonmagnetic soil is of great significance when the electromagnetic compatibility is concerned. To evaluate the earth return impedance accurately and efficiently, a semianalytical approach is proposed in this paper. With the proposed approach, the expression of the earth return impedance, which includes a complex highly oscillatory integrand, is divided into two parts, i.e., the definite and the tail integral. The definite integral is evaluated by using the moment technique and the tail integral is evaluated by using the exponential integrals with an asymptotic integrand. The numerical examples show that the proposed algorithm can evaluate the earth return impedance with various parameters and arbitrary conductor arrangements accurately and efficiently and the required computational time of the proposed approach is almost independent of the geometric and electric parameters.

A semianalytical inverse Fourier transform, which can evaluate the time response at arbitrary time, is proposed. The basic idea is fitting the response in frequency domain by a sum of piecewise cubic spline functions with an adaptive sampling strategy, and the response in time domain is evaluated with the help of the moment functions to avoid calculating the highly oscillatory integral. A recursive algorithm is derived, which can efficiently calculate the moment functions with different ranks. As an application of the proposed approach, the underground horizontal electric field of a lightning channel is evaluated in the time domain. In comparison with the results in the published literature, the numerical examples show that the proposed approach can save the computational time at least 50 times compared to the one using a conventional inverse Fourier transform technique. The proposed approach, in fact, can be generalized to apply to other scenarios when the inverse Fourier transform is involved.

A combined method adopting the domain decomposition is proposed for analyzing the ion-flow field of high-voltage direct current transmission lines, including the effect of the transverse wind. The upstream finite-element method is used with a dense triangle mesh in the vicinity of bundle conductors to guarantee the accuracy. The upstream finite-difference method is proposed and the larger uniform quadrilateral grid is applied to simulate the ion-flow field in the rest of the region with a satisfactory precision. The calculation process of the Poisson equation is iterated with the Dirichlet–Neumann algorithm to coordinate the solution between adjacent subdomains. The proposed approach improves the efficiency and remains stable with high wind speed. Finally, the influence of wind on the ion-flow field is analyzed and calculations are in good agreement with experimental data and results in the previous literature.

Purpose – The per-unit-length earth return mutual impedance of the overhead conductors plays an important role for analyzing electromagnetic transients or couplings of multi-conductor systems. It is impossible to have a closed-form expression to evaluate this kind of impedance. The purpose of this paper is to propose an efficient numerical approach to evaluate the earth return mutual impedance of the overhead conductors above horizontally multi-layered soils. Design/methodology/approach – The expression of the earth return mutual impedance, which contains a complex highly oscillatory semi-infinite integral, is divided into two parts intentionally, i.e. the definite and the tail integral, respectively. The definite integral is calculated using the proposed moment functions after fitting the integrand into the piecewise cubic spline functions, and the tail integral is replaced by exponential integrals with newly developed asymptotic integrands. Findings – The numerical examples show the proposed approach has a satisfactory accuracy for different parameter combinations. Compared to the direct quadrature approach, the computational time of the proposed approach is very competitive, especially, for the large horizontal distance and the low height of the conductors. Originality/value – The advantage of the proposed approach is that the calculation of the highly oscillatory integral is completely avoided due to the fact that the moment function can be evaluated analytically. The contribution of the tail integral is well included by means of the exponential integral, though in an asymptotic way. The proposed approach is completely general, and can be applied to calculate the earth return mutual impedance of overhead conductors above a soil structure with an arbitrary number of horizontal layers.

An efficient approach to evaluate the radiated electromagnetic field of a lightning channel over a horizontally stratified conducting ground is proposed in this paper. The electromagnetic field component produced by a lightning channel, expressed in the form of generalized Sommerfeld integral (GSI) with a complicated integrand, is calculated along a newly proposed path in the complex plane. Due to the change of the integration path, the integrand in the GSI turns out to decay dramatically fast and without any oscillation at all. As explained in this paper, the larger horizontal distance will become the benefit to achieve a quicker convergence, which is just opposite to the case that the integration path is along the real axis. The validity of the proposed methodology is justified by the extensive comparison with the results in other publications. As a matter of fact, the methodology in this paper can be generalized to evaluate stratified conducting ground with any number of layers.

PurposeA fast algorithm is proposed to calculate the lightning electromagnetic field over a perfectly conducting earth surface.Design/methodology/approachThe channel base current is approximated by a number of sub‐domain quadratic functions using the proposed adaptive sampling technique, and the derivative and integral of the channel base current with respect to time can be analytically expressed. With the help of these approximations, the ideal electromagnetic field of the lightning channel can be evaluated along the lightning channel with respect to the height.FindingsThe computational time can be greatly reduced using the proposed approach to evaluate the electromagnetic field of a lightning channel in the time domain.Originality/valueThe adaptive sampling technique is a general‐purposed approach, which can be potentially used in other applications to fit a function with the minimal number of intervals.

The radiated horizontal electromagnetic field of a lightning channel acts as the excitation when the lightning-induced voltages on overhead lines are under study. To accelerate the calculation of the horizontal electric field of a lightning channel, a piecewise Hermite interpolation model is proposed, which exploits the distinct feature of the transmission line whose height keeps unchanged. In the piecewise Hermite interpolation model, the key technique is fast evaluating the derivative of the horizontal electric field expressed by the generalized Sommerfeld integral. In this paper, the moment technique is utilized to calculate the derivatives efficiently. As demonstrated in the numerical examples, the piecewise Hermite interpolation model can reach a high accuracy with a very low computation cost.

The evaluation of the electromagnetic field radiated by a lightning stroke channel is a necessary step for the analysis of many electromagnetic compatibility problems. An efficient algorithm for calculating the electromagnetic field of a lightning stroke channel is presented in this paper. The electromagnetic field of a lightning stroke channel, expressed by the generalized Sommerfeld integral, is decomposed into two parts. One is a definite integral, which can be evaluated using the proposed moment technique to avoid the troublesome oscillatory integral; the other is an improper integral with an infinite upper limit, which is calculated with the newly developed asymptotic expression to reach convergence quickly. The proposed approach turns out to be very efficient. The numerical examples validate the proposed approach in both frequency and time domain.

The Cooray-Rubinstein formula has been widely utilized for evaluating the horizontal component of the electric field generated by a lightning return stroke. A fast time-domain implementation of Cooray-Rubinstein formula in time domain, by means of the piecewise quadratic convolution technique and the use of a quadrature routine of a truncated integral instead of polynomial approximations of the Bessel functions, is presented in this paper. The advantages of the proposed approach can be summarized as follows. First, the issue of the numerical overflow and the cancellation error for calculating the lightning horizontal electric field is avoided; second, the horizontal electric field of a lightning can be evaluated quickly, because the convolution has been expressed in a closed-form expression. The numerical examples demonstrate the efficiency and validity of the proposed approach.

Purpose A fast algorithm is proposed to calculate the lightning horizontal electric field over a lossy ground. Design/methodology/approach The lightning horizontal electric field in frequency domain is approximated by a number of piecewise cubic polynomial functions by using the proposed adaptive Hermite strategy. To utilize the Hermite strategy, the frequency domain spectrum and its derivative with respect to frequency are required. The integral kernel of the derivative appears singular along the real axis. To overcome this singularity and accelerate the calculation, a new integration path is proposed. With the help of the Hermite interpolation model and the new path, the lightning horizontal electric field in time domain can be obtained rapidly. Findings The singularity problem has been overcome with the new integration path and the adaptive Hermite strategy proposed in this paper is at least 50 times faster than the one using the equally spaced sampling approach. Originality/value The adaptive Hermite approach can be a good candidate for fitting a wideband frequency domain response and the revised new integration path can be utilized when the calculation of the generalized Sommerfeld integral (GSI) or its derivative with respect to frequency is involved.

A fast approach for evaluating the magnetic field in air generated by an underground conductor is proposed in this paper. By means of the asymptotic extraction technique, the magnetic field can be decomposed into two parts. One is the contribution from the asymptotic integrand, which can be calculated analytically; and the other can be expressed by a sum of the definite integral and the exponential integrals. Due to the fact that there is no improper integral involved, the approach proposed here is highly efficient. Meanwhile, the impact of the eddy current to the magnetic field is quantitatively analyzed. The proposed approach could be used in the electromagnetic environment assessment for underground power cable systems.

Electrochemical oxidation effects of the tube type electrolysis module system were investigated for the treatment of industrial wastewater. The tube type electrolysis module consisted of a rod anode and an outer tube cathode. Materials used for the anode were titanium electroplated with RuO 2 and IrO 2 respectively. Stainless steel was used for the cathode. Chlorate production was one of major factors in electrochemical oxidation of tube type electrolysis module system used in this research. Chlorine conversion from chloride to chlorate occurred at a rate of 66.8 mg/L for the textile wastewater and 75.7 mg/L for the pharmaceutical wastewater over a 60 min retention period. Chlorine gas concentration was 360 ppm for the textile wastewater and 500 ppm for the pharmaceutical wastewater after a 60 min electrolysis period. Specific energy consumption was measured during the electrolytic process with the Ti/RuO 2 anode and the Ti/IrO 2 anode. The range of specific energy consumption was 0.064–0.108 kW h/gCOD Cr for the Ti/RuO 2 anode over the variation range of hydraulic retention time. The Ti/RuO 2 anode had advantages in the electrolytic wastewater treatment with lower specific energy consumption.

This paper proposes a novel sensorless drive method for the brushless DC (BLDC) motors. It provides an accurate and robust position and speed estimation from the near-zero speed to the rated speed. The proposed sensorless algorithm uses a trapezoidal waveform of the backelectromotive force (EMF) signal with speed information. The back-EMF signals are estimated based on the three-phase current and terminal voltage signals. The validity of the proposed method is verified through both simulation and experimental results

The electromagnetic fields generated by a vertical electric dipole, expressed in the form of the Sommerfeld integral, are important in the study of lightning. In this paper, an algorithm, which can analytically approximate the Sommerfeld tail integral, is proposed. Due to the fact that the tail integral is expressed by a sum of several error functions, the tail integral of a vertical electric dipole can be evaluated without the truncation of the infinite upper limit. The comparison indicates that the results calculated by the proposed algorithm are accurate, and the computational time, compared to the one using direct numerical quadrature method, is much shorter.

PurposeThe purpose of this paper is to present an original iterative nodal approach to calculate the fault current distribution on overhead lines.Design/methodology/approachBy changing the mutual couplings among different conductors into the equivalent voltage sources, node voltages are updated iteratively by using conventional nodal analysis with those additional sources until the convergence is achieved.FindingsThe proposed algorithm can handle the complicated topology of a power transmission line and has no difficulties in taking all physical couplings into account. The fault current distribution calculated by this method is in good agreement with those published in the literature. Although the proposed approach is iterative, the CPU time needed is still reasonable compared to the direct solution approach. The memory requirement is low because the coefficient matrix is highly sparse for the nodal analysis of each iteration loop.Originality/valueThe proposed approach can serve as an alternative in calculating the fault current because of its efficiency and ease of implementation.

The earth-return impedance of underground conductors, whose expression was first derived by Pollaczek, is of particular importance for the study of the electromagnetic compatibility problems among the underground conductor system. In this paper, a fast and highly accurate algorithm is presented to calculate the Pollaczek's integral. The high accuracy acquired by the proposed procedure is due to the fact that the tail of the Pollaczek's integral is approximated by a sum of several exponential integrals, which in nature means that there is no truncation to the Pollaczek integral. The extensive comparison with published data indicates that the proposed algorithm is highly accurate and the computational time is reasonable.

It is very essential to calculate the mutual impedance between overhead and buried conductors for analyzing electromagnetic compatibility problems related to a transmission line system. An efficient algorithm for calculating the Pollaczek integral, whose integrand oscillates rapidly and decays slowly, is proposed in this paper. With the help of the asymptotic extraction technique, the Pollaczek integral can be decomposed into the sum of two parts, one of which is expressed with an exponential integral and the other is the one that has a rapidly damped integrand. A comparison of the numerical results with published data shows very good agreement. The proposed approach is a good candidate for calculating impedances related to the Pollaczek integral.

The objectives of this study are to investigate characteristics of electrochemical oxidation of wastewater depending on electrode materials and to analyze the influence of the chloride ion as an electrolyte on electrochemical oxidation of pigment wastewater using a Ti/IrO 2 tube-type electrode. The Ti/IrO 2 electrode was adopted as the most proper material in the comparative analysis under COD removal efficiency and current efficiency. The current efficiency for each electrode material was decreased in the order of Ti/IrO 2 16.5%, Ti/Pt 14.0%, and graphite 3.4%. Two kinds of electrolytes of NaCl and Na 2 SO 4 revealed different levels of electrochemical oxidation under the same conductivity conditions. Specific energy consumption was reduced by adding a chloride ion in the electrochemical oxidation treatment. The chlorite ion (ClO 2 - ) and free chlorine were produced in the Ti/IrO 2 tube-type electrochemical oxidation systems. The production amount of chlorite ion was larger than double that of free chlorine production. The indirect oxidation process by the intermediate product was concluded to be the major principle for COD removal.

This paper describes an efficient numerical approach for the calculation of the per-unit length earth-return impedance of a conductor inside a tunnel. The influence of the tunnel on the per-unit length impedance is replaced by a set of equivalent current sources via the fictitious medium method. The main advantage of the proposed approach is that it can solve the boundary value problem within the tunnel region. The proposed method can reduce the calculation region and, thus, leads to time savings. A comparison of the numerical results with published data shows very good agreement. The proposed method is a good candidate for impedance calculation of a conductor inside a tunnel.

In this paper, a simulation model is proposed to evaluate the electromagnetic transient surge current distribution in a lightning protection system (LPS) due to a direct lightning stroke. The model is based on the coupled transmission line network in the frequency domain combined with the Fourier transform technique. The conductor of the LPS is described using the coupled transmission line model, and can be reduced to an active two-port equivalent circuit. The unknown quantities are the node voltages of the LPS at the physical junction, which leads to a fast solver at each frequency. The validation of the proposed approach is performed by comparing the results with those in the technical literature. The numerical examples show the flexibility, efficiency, and accuracy of the model in the range of practical application of LPS.

A novel stator flux and current estimator is proposed to estimate stator flux and remove dc offset error in induction motor with offsets of measured currents. The proposed stator flux estimator is able to solve the problem related with a pure integrator to estimate stator flux in induction motor for operating in a wide speed range and the proposed current estimator is able to remove offsets of measured currents. Normally a drift is made by integration of dc offset error present in the estimated stator flux due to DC offset in the measurement of phase current. The estimator can be able to solve a problem related the pulse with modulation (PWM) signal which is the signal is not sinusoidal signal.

The design of grounding system often relies on the performance simulations. The evaluation of the current distribution of grounding system for many frequencies by using the method of moments (MoM) may take a long time since the impedance matrix must be recomputed at each new frequency. A multiobject adaptive spatial sampling approach is presented to construct the fitted model of the electric field intensity generated by a horizontal electric dipole. The [Z] matrix spatial interpolation technology with MoM is described to reduce the computational time needed for the transient characteristics analysis of a horizontal grounding system. The accuracy and computational time of the [Z] matrix interpolation method are compared with those of the direct MoM. The numerical examples show that the [Z] matrix spatial interpolation method can reduce the computation requirement effectively

Soil ionization has a great effect on the performance of grounding electrodes fed by currents of high magnitude. In this paper, a numerical method is proposed to analyze the transient performance of grounding system, which takes account of the dynamic and nonlinear effects of soil ionization. The method couples moment method with circuit theory and Fourier transform. The transient performance of grounding system considering the soil ionization effect is compared with that not considering soil ionization effect.

How to precisely measure the grounding impedance of large-scale substations is a fundamental guarantee for the safe operation of power systems. If the ground wires were connected to the grounding grid, these ground wires would shunt a part of the injected measuring current and allow the measured grounding impedance to be smaller than the actual impedance of the grounding system. Based on an actual 500-kV grounding system, this paper discusses how to analyze the influence of the overhead ground wire on the measured grounding impedance and how to obtain the real grounding impedance of the grounding system. A numerical analysis model considering the grounding system, the transmission lines, towers, and their grounding devices, based on the multilayer soil model analyzed from field test data of apparent soil resistivity, was constructed to analyze the influence of ground wires and tower grounding resistances on grounding impedance, and the general effects of different parameters, such as tower impedance, grounding impedance, and circuits of transmission lines, were analyzed. The real grounding impedance of the substation with connected overhead ground wires was validated, and some useful results have been obtained, based on the field-measured values and numerical analysis.

The shielding failure is the occurrence of a lightning stroke that bypasses the overhead ground wires and terminates on the phase conductors. The correct design to improve the shielding effect of transmission line to lightning is one of the key problems of transmission line design. A numerical analysis model for shielding failure of transmission line based on electromagnetic field theory is proposed in this paper. The electrical field of the system including lightning leader, transmission line and ground is solved, the range of lightning current striking the phase conductor is obtained, and the shielding failure probability of transmission line is calculated. The lightning leader model and the critical breakdown electrical field intensity of long gap are discussed. The analyzed results by numerical analysis model are compared with those by the electrogeometric model.

In a high soil resistivity area, counterpoise wires are applied to decrease the grounding resistance of tower grounding devices. If the conductor of counterpoise wire is very long, although the power frequency grounding resistance of the tower grounding device is decreased, the lightning protection performance of the transmission line is still not good. The influences of the length of grounding electrodes on the lightning transient characteristic were analyzed. The dynamic and nonlinear effect of soil ionization around the grounding electrode was considered in the analysis model of transient characteristics for the grounding electrodes under lightning impulse. The counterpoise wire has an effective length when lightning passes through it. When the length of a grounding electrode exceeds the effective length, the grounding conductor will not be utilized effectively. The simulating experiments were performed to analyze influences of the length of the counterpoise wire on the impulse characteristics. The formulae to calculate the impulse effective lengths of counterpoise wires were proposed. The model proposed in the paper has been validated by comparing the numerical results with experimental tests.

A two-stage algorithm is presented to determine an analytical model-based rational function by adaptively selecting sampling points. At the first stage, the rational interpolation function is created by using Stoer-Bulirsch algorithm and comparing the fitted model with the different ranks. At the second stage, the fitted model is validated by comparing with the first-principle model at a set of checking points. Some checking points will be added to the sampling series determined in the first stage to improve the fitted model. The new proposed algorithm is more accurate and effective than that using Stoer-Bulirsch interpolation only due to the fact that it appends the validation approach. When a highly oscillating curve is approximated, the validation ensures the fitting precision. With the two-stage MBPE algorithm, some time-consuming electromagnetic computations can be replaced by the interpolation from the fitting functions, which can increase the computational efficiency greatly. This method i...